Short answer. In addition to colder, drier air, you have more uninterrupted viewing hours, depending how far you are removed from the equator. Here at 45 deg N, winter nights start early and end late. The seasons are reversed for the southern hemisphere, but the principle is the same.

Summer nights are very short in comparison, and the extra moisture and haze can reduce the contrast and clarity of the skies.

Now since i've been thinking about it. Perhaps it also has something to do with the winter stars and constellations too. e.g. the brightest star, Sirius, is a winter star, well, yeah, as in northern hemisphere.

Yes, there are some bright winter stars. Also, don't forget, that in the winter, we are looking in a completely different direction than in summer....the nightime sky is facing toward the outer edge of the Milky way, whereas in summer, it faces in the direction of the galaxy's center, whereby the light of much more stars in that summer direction obscures the sky with a lighted haze. This in addition to pollution and more moisture content in the lower atmosphere.

It is of course very weather dependent. Here in the Pacific Northwest we have a very high percentage of cloudy days and nights in the winter, fall and spring, while our summers have generally clear skies. Consequently, I have spent a lot more time looking up in the summer.

Statistically speaking, when your best skies are is location dependent. It's true that the atmosphere is much more stable in winter and you have a longer night to work with, but this does not necessarily imply the best observing. I know that here in Ithaca we get the highest proportion of clear nights in the fall, so that is the best time for observing for us. Especially in a region like this, the geography and microclimates have a lot to do with it.

A cold, still, cloudless night is ideal. Here in the midwest we average a handful of such nights per month in the winter. In my experience, I have found latex gloves over thin leather golf [or silk/satin] gloves, and paper or plastic bags between cotton socks will keep the extremeties warm.

I live in the Northeast USA, and in the same week, a clear, warm, moist day is inferior to a dry, cold, also clear day. The big factor that beats my stargazing though, is light pollution; clouds and moisture don't help that.

I found a little cloud usually accompanies better seeing to be honest. Dont forget its also nice and warm in the summer too. I had 1/4" of ice on my OTA last time I took it out. Light pollution is ridiculous here in Holland too.